Chapter 1

Mathematical Thinking

Mathematics is both the queen and the handmaiden of all sciences—Eric Temple Bell.

It would be great if we could study the physical world unencumbered by the need for higher mathematics. This is probably the way it was for the ancient Greek natural philosophers. Nowadays, however, you can’t get very far in science or engineering without expressing results in mathematical language. This is not entirely a bad thing, since mathematics turns out to be more than just a language for science. It can also be an inspiration for conceptual models which provide deeper insights into natural phenomena. Indeed the essence of many physical laws is most readily apparent when they are expressed as mathematical equations—think of ...

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